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16 May, 12:37

A boat has a mass of 4900 kg. Its engines generate a drive force of 4600 N due west, while the wind exerts a force of 670 N due east and the water exerts a resistive force of 1170 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign?

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  1. 16 May, 13:03
    0
    a = + 0.56 m/s² (due west)

    Explanation:

    We apply Newton's second law:

    ∑Fx = m*a (Formula 1)

    ∑F : algebraic sum of the forces in Newton (N)

    m : mass in kilograms (kg)

    a : acceleration in meters over second square (m/s²)

    dа ta:

    m = 4900 kg

    Fd = 4600 N : drive force

    Fw = 670 N : wind force

    Fr = 1170 N : water resistive force

    Problem development

    We apply the formula (1)

    ∑Fx = m*a

    Fd-Fw-Fr = m*a

    4600 - 670 - 1170 = 4900 * a

    2760 = 4900 * a

    a = (2760) / (4900)

    a = + 0.56 m/s² (due west)
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